Analytical model predicting the concrete tensile stress development in the restrained shrinkage ring test

Concrete structures may experience unexpected cracking at an early age. Early age cracking can be induced by restrained deformations where tensile stress generated in concrete exceeds its tensile strength. The restrained concrete ring test is often used to evaluate the ability of concrete to resist early age cracking induced by shrinkage. This paper proposed an analytical model of the restrained ring test by capturing the effect of both restrained shrinkage and tensile creep based on the age-adjusted effective modulus theory. The analytical model allows for accurately predicting the tensile stress of the restrained concrete ring based on the experimental measurements of the time-dependent development of elastic modulus, total free shrinkage, and tensile creep of concrete. A numerical finite element simulation was also successfully carried out to validate the new analytical model. Importantly, the model was validated considering a total of 21 concretes consisting of 6 strength grades ranging from 25 MPa to 100 MPa. For each grade, one fly ash blend (30%), two GGBFS blends (40% and 60%) and a reference mix without supplementary cementitious materials were tested.